A UCLA researcher claims that the life span of mice can be extended by as much as 25% when the calories in their diet are reduced by approximately 40% from the time they are weaned. The restricted diet is enriched to normal levels by vitamins and protein. Assuming that it is known from previous studies that σ = 5.6 months, how many mice should be included in the sample if we wish to be 99% confident that the mean life span of the sample will be within 2 months of the population mean for all mice subjected to this reduced diet? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The required sample size is ☐ . (Round up to the nearest whole number as needed.) Areas under the Normal Curve Area Areas under the Normal Curve .03 .04 -1.2 -1.1 0.3015 2 .00 .01 .02 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.3 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.0006 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 -3.1 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0019 0.0021 -2.8 0.0020 0.0035 0.0033 0.0031 0.0030 0.0029 -2.7 0.0027 0.0034 0.0032 0.0028 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.5 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4 -2.3 0.0107 0.0104 0.0099 0.0102 0.0091 0.0096 0.0094 0.0087 0.0089 0.0084 -2.3 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2 -2.1 0.0179 0.0166 0.0162 0.0158 0.0154 0.0150 0.0143 -2.1 0.0174 0.0170 0.0146 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0 -1.9 0.0287 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 0.0281 -1.9 0.0274 0.0359 -1.8 0.0344 0.0351 0.0336 0.0329 0.0307 0.0322 0.0301 0.0314 0.0294 -1.8 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 -1.7 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0516 0.0537 0.0465 0.0526 0.0455 -1.6 0.0505 0.0495 0.0485 0.0475 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 0.0808 0.0793 0.0764 -1.4 0.0721 0.0708 0.0778 0.0681 0.0749 -1.4 0.0735 0.0694 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 0.1131 0.1151 0.1112 0.1093 0.1056 0.1075 0.1038 0.1003 0.0985 -1.2 0.1020 0.1335 0.1314 0.1357 0.1251 0.1292 0.1271 0.1230 0.1210 0.1190 -1.1 0.1170 0.1539 0.1423 -1.0 0.1587 0.1562 0.1515 0.1492 0.1469 0.1446 0.1379 0.1401 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.2389 -0.7 0.2420 0.2266 0.2358 0.2236 0.2327 0.2296 0.2206 0.2177 -0.6 0.2743 0.2709 0.2643 0.2578 0.2546 0.2514 0.2483 0.2676 0.2611 -0.5 0.3085 0.3050 0.2946 0.2912 0.2981 0.2810 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 -0.3 0.3783 0.3745 0.3707 0.3632 0.3821 0.3669 0.3594 0.3557 0.3520 -0.2 0.4207 0.4090 0.4168 0.4129 0.4052 0.4013 0.3974 0.3936 0.3897 0.4602 0.4522 0.4483 0.4443 -0.1 0.4364 0.4562 0.4325 0.4404 0.4286 0.4960 0.4801 -0.0 0.4721 0.5000 0.4920 0.4880 0.4840 0.4761 0.4681 .00 .01 .02 .03 .04 .05 .06 .07 .08 .05 .06 .07 .08 .09 Z .00 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4 0.0 0.1 0.0004 0.0006 0.2 0.3 0.4 .01 .02 .03 .04 .05 .06 .07 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.6103 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6141 0.2 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6480 0.6406 0.6443 0.3 0.6517 0,6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 .08 .09 名 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 -2.7 0.7 0.7257 0.7580 0.8 0.7881 0.9 0.8159 1.0 0.8413 0.9726 0.7291 0.7324 0.7357 0.7611 0.7673 0.7642 0.7910 0.7939 0.7967 0.8186 0.8212 0.8238 0.8438 0.8461 0.8485 0.8508 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.9066 0.9099 1.3 0.9131 0.9032 0.9049 0.9082 0.9115 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 1.5 0.9345 0.9357 0.9370 0.9332 0.9382 0.9394 0.9406 0.9463 0.9505 1.6 0.9515 0.9452 0.9474 0.9484 0.9495 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 1.8 0.9656 0.9664 0.9641 0.9649 0.9671 0.9678 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.5 0.7389 0.7422 0.7454 0.7486 0.7549 0.7517 0.6 0.7794 0.7823 0.7852 0.7704 0.7 0.7734 0.7764 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8790 1.1 0.8810 0.8830 0.8980 0.8997 0.9015 1.2 0.9177 0.9147 0.9162 1.3 0.9292 0.9306 0.9319 1.4 0.9686 0.9750 2.0 2.1 2.2 0.9861 0.9864 0.9772 0.9783 0.9778 0.9821 0.9826 0.9830 0.9868 2.3 0.1611 -0.9 0.9893 0,9896 2.4 0.9918 0.9920 2.5 0.9938 0.9940 0.9898 0.9922 0.1894 0.1867 -0.8 0.2148 -0.7 0.2451 -0.6 0.2776 -0.5 0.3121 0.3483 0.3859 0.4247 0.4641 -0.0 .09 -0.4 -0.3 -0.2 -0.1 2 ▲ B' \' C']' σ' 2.6 0.9957 0.9927 0.9929 0.9943 0.9945 0.9946 0.9959 0.9960 0.9931 0.9429 0.9418 0.9441 1.5 0.9525 0.9535 0.9545 1.6 0.9616 0.9625 0.9633 1.7 0.9699 0.9693 0.9706 1.8 1.9 0.9756 0.9761 0.9767 0.9788 2.0 0.9798 0.9803 0.9793 0.9817 0.9808 0.9812 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 0.9884 0.9887 0.9871 0.9875 0.9878 0.9881 0.9890 2.2 0.9913 0.9901 0.9904 0.9906 0.9909 0.9911 0.9925 0.9932 0.9934 0.9916 2.3 0.9936 2.4 ¡Ai --‹ ›0 = 0 2.7 2.8 2.9 3.4 2 .00 0.9941 0.9956 0.9953 0.9955 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9974 0.9976 0.9975 0.9977 0.9977 0.9979 0.9978 0.9981 0.9982 0.9982 0.9983 0.9984 0.9985 0.9986 2.9 0.9984 0.9985 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 3.1 0.9990 0.9993 0.9991 0.9991 0.9992 0.9992 0.9991 0.9993 3.1 0.9992 0.9992 3.2 0.9993 3.2 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 3.3 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 .01 .02 .03 .04 0.9948 0.9949 0.9951 0.9952 2.5 0.9961 0.9962 0.9963 0.9964 2.6 0.9972 0.9973 0.9974 2.7 0.9979 0.9980 0.9981 2.8 0.9986 0.9997 3.3 3.4 .05 .06 .07 .08 .09